TY - JOUR
T1 - General sum-connectivity index of unicyclic graphs with given diameter
AU - Alfuraidan, Monther Rashed
AU - Das, Kinkar Chandra
AU - Vetrík, Tomáš
AU - Balachandran, Selvaraj
N1 - Publisher Copyright:
© 2021 Elsevier B.V.
PY - 2021/5/31
Y1 - 2021/5/31
N2 - For α∈R, the general sum-connectivity index of a graph G is defined as χα(G)=∑uv∈E(G)[degG(u)+degG(v)]α, where E(G) is the edge set of G and degG(v) is the degree of a vertex v in G. Let Un,d be the set of unicyclic graphs with n vertices and diameter d.We present the graph with the smallest general sum-connectivity index among the graphs in Un,d for −1≤α<0 and the graph with the largest general sum-connectivity index among the graphs in Un,d for 0<α<1. Sharp lower bounds on the classical sum-connectivity index and the harmonic index for graphs in Un,d follow from the lower bound on the general sum-connectivity index.
AB - For α∈R, the general sum-connectivity index of a graph G is defined as χα(G)=∑uv∈E(G)[degG(u)+degG(v)]α, where E(G) is the edge set of G and degG(v) is the degree of a vertex v in G. Let Un,d be the set of unicyclic graphs with n vertices and diameter d.We present the graph with the smallest general sum-connectivity index among the graphs in Un,d for −1≤α<0 and the graph with the largest general sum-connectivity index among the graphs in Un,d for 0<α<1. Sharp lower bounds on the classical sum-connectivity index and the harmonic index for graphs in Un,d follow from the lower bound on the general sum-connectivity index.
KW - Diameter
KW - General sum-connectivity index
KW - Unicyclic graphs
UR - https://www.scopus.com/pages/publications/85101535608
U2 - 10.1016/j.dam.2021.02.012
DO - 10.1016/j.dam.2021.02.012
M3 - Article
AN - SCOPUS:85101535608
SN - 0166-218X
VL - 295
SP - 39
EP - 46
JO - Discrete Applied Mathematics
JF - Discrete Applied Mathematics
ER -